MATLAB: Fitting two Parameters to an equation with data

Question

Hello, I've been stumped trying to solve this problem for a while now and was hoping someone here might be able to help. For background info I'm not completely new to MATLAB, I have a good understanding of the fundamentals and I've developed scripts and functions to run things like Newton-Rhapson method etc…

I have a set of data:

x=[0;69.18248;78.63425;83.30743;86.66291;87.06997]; t=[0;1;2;3;4;5];

And I want to fit an equation to this data. I have the equation shown below:

x= 1 – 0.5584*exp(-a*t) – 0.4416*exp(-b*t)

As you can see, I have the x data points for each t value. I do not, however, know the constant parameters a and b. I wish to find a value for them that will best fit this data. I've looked around for a solution and some say it might be possible using fminsearch but I don't understand how to set up the functions required to do so. Any help is much appreciated.

Answer 1

 y=1-x;
 fun=@(ab) abs( .5584*exp(-ab(1)*t)+.4416*exp(-ab(2)*t)  - y);
 ab=fminsearch(fun,[0,0])
 a=ab(1);
 b=ab(2);